Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×M16×C61 ⋊ C4 |
| Sylow | C61 ⋊ C2×#344 |
388 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=e,b^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^50,e^b=eg,h^b=h^11,h^c=h^60,h^e=h^60,h^f=h^60344 conjugacy classes — view the full character table.
| maximal subgroup of | #344×#6923, #30602339, #30602459, … |
| maximal normal subgroup of | #344×#6923, #30602339, #30602459, … |
| maximal quotient of | #30596275, #30596278, #30596283, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20222);